Complex symmetry and cyclicity of composition operators on $H^2(\mathbb{C}_+)$

S. Waleed Noor; Osmar R. Severiano

Complex symmetry and cyclicity of composition operators on $H^2(\mathbb{C}_+)$

Functional Analysis 2019-10-14 v2

Authors: S. Waleed Noor , Osmar R. Severiano

Abstract

In this article, we completely characterize the complex symmetry, cyclicity and hypercyclicity of composition operators $C_\phi f=f\circ\phi$ induced by affine self-maps $\phi$ of the right half-plane $\mathbb{C}_+$ on the Hardy-Hilbert space $H^2(\mathbb{C}_+)$ . We also provide new proofs for the normal, self-adjoint and unitary cases and for an adjoint formula discovered by Gallardo-Guti\'{e}rrez and Montes-Rodr\'{i}gues.

Keywords

composition operators cyclic homology operator theory

Cite

@article{arxiv.1908.08592,
  title  = {Complex symmetry and cyclicity of composition operators on $H^2(\mathbb{C}_+)$},
  author = {S. Waleed Noor and Osmar R. Severiano},
  journal= {arXiv preprint arXiv:1908.08592},
  year   = {2019}
}

Comments

8 pages, to appear in Proc. Amer. Math. Soc

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